Q&A: Thoughts on the Dice Analogy for the Multiverse and Choosing Between Hypotheses
Thoughts on the Dice Analogy for the Multiverse and Choosing Between Hypotheses
Question
With God's help,
Hello, honorable Rabbi! Happy Purim for those in walled cities 🙂
Sorry for writing briefly, but I hope the Rabbi will actually prefer it that way.
When we are faced with a unique phenomenon, there are three ways to explain it: 1. It is a coincidence. 2. There were many attempts behind it (multiverse). 3. There was a cause that brought it about (God).
The standard example against the second claim, that there were many attempts, is that if nowadays we saw someone throwing many dice and they all came up 6-6. But I wanted to ask: why should we really be surprised by that? After all, throughout human history there have in fact been enough occasions when people threw dice, so it is obvious that such a case would certainly happen. So why should we really be astonished by it?
Also, I wanted to ask about the argument itself. When we look at the world and do not know whether parallel worlds exist or not, and we also do not know whether there is a God or not, and let us assume that both have equal explanatory power regarding the phenomenon—if so, what would make us prefer one hypothesis over the other? I thought perhaps Occam's razor, but it is not at all clear whether this is a normative tool or whether it actually has factual force.
Thank you very much, and happy Purim for those in unwalled cities.
Answer
It depends how many times the dice came up six. If it happened a hundred times in a row, that is not plausible, because there have not been enough throws throughout history to make that plausible. Beyond that, if there is a possibility that the die is loaded, that sounds like a more reasonable explanation than a case that happens after a huge number of throws. If there is no other explanation, then perhaps we really would accept the claim that it is just chance.
In my book I explained that this is based on a consideration of simplicity (Occam). My position is that the razor principle deals with the world itself and is not merely a methodological tool of ours. See my article here:
Discussion on Answer
Thanks for the reference; I read it, but I have an objection to the very idea that simplicity leads to truth, even empirically. I once heard from a friend why this principle is not well founded.
For example, when we are faced with a sick person who has ten different symptoms that can be explained in only two ways: either this is a disease called A, whose chance of occurring is 1 in a million, or it is the combined probability of two diseases B+C, where the chance of each one occurring is 1 in a thousand.
Statistically there is no preference for one theory over the other, but according to Occam's razor we would prefer to say it is one disease, A. But since there is no statistical preference for that, it only shows that this is a tool that is not really useful or correct.
The basis of Occam's razor does not come from what the mind or the eye sees; rather, it usually comes from statistical preference. For example, like Rabbi Chaim's parable about the fool.
The question is what counts as simplicity. Obviously, the criterion of simplicity chooses among theories that are equivalent in every other respect. Quantum theory is clearly not the simplest theory imaginable, and the same is true of relativity. Among the theories that explain the facts, these are the simpler ones. The same applies here.
By the way, in my article I showed why it is necessary to say that the razor is a correct principle and not merely a useful one.
So the Rabbi thinks it is indeed preferable to argue that disease A is what causes the patient's symptoms rather than the combination of B+C?!? That sounds very, very puzzling.
I saw the claim you mentioned about the laws of nature and the straight line that runs through them, but the fact is that Newton's laws are indeed not correct in light of the newer theories of quantum mechanics; they are only an approximation. So that shows that simplicity is not necessarily connected to truth.
If I knew nothing about the three diseases and saw some symptoms, I would certainly prefer an explanation that they stem from one disease whose rarity is 1 in a million over an explanation that attributes them to two different diseases whose rarity is 1 in 1,000. Once those diseases are already known, your whole calculation is irrelevant, because their rarity in the general population is irrelevant to deciding their likelihood in someone who has developed those symptoms. The calculation is simply not defined.
What you said at the end is simply mistaken. Newtonian mechanics is still correct today at low speeds. It did not turn out that we were wrong about the relation between force and acceleration. It really is a straight line. (By the way, this is not quantum mechanics but mainly relativity.)
I did not understand why this is not defined, and why once the rarity in the population is already known one cannot infer from that to an individual person.
But in any case, in the article there you presented that the only way to ground the razor principle is through the versalist approach that supposedly softens the gap between thought and cognition.
But it is not clear how the Rabbi uses that same "ideal" proof for the case at hand, which is a hypothetical case that does not exist in reality at all. It is not like laws of nature, where you can argue that you "see" them. Because in our case, one can assume that there could be a reality in which several diseases together produce the symptoms instead of one disease, so how has the Rabbi already seen in advance what has not happened?
And therefore I think this is an ad hoc assumption.
Because the rarity is in the population as a whole, not among those who suffer from the specific symptoms before you. When a defendant accused of murder comes before you as a judge, can you acquit him because the probability that a person is a murderer is negligible? That is a mistake, because the reason he is brought before you is that there is some evidence linking him to the murder. Among those for whom there is evidence linking them to the murder, the probability that one of them is the murderer is higher.
I did not understand the second question.
Thanks for the reference; I read it, but I have an objection to the very idea. I once heard from a friend why this principle is not well founded.
For example, when we are faced with a sick person who has ten different symptoms that can be explained in only two ways: either this is a disease called A, whose chance of occurring is 1 in a million, or it is the combined probability of two diseases B+C, where the chance of each one occurring is 1 in a thousand.
Statistically there is no preference for one theory over the other, but according to Occam's razor we would prefer to say it is one disease, A. But since there is no statistical preference for that, it only shows that this is a tool that is not really useful or correct.
The basis of Occam's razor does not come from what the mind or the eye sees; rather, it usually comes from statistical preference. For example, like Rabbi Chaim's parable about the fool.